TOPEKA, Kan.—Two years ago, Kansas Gov. Sam Brownback laid out an aggressive program of tax cuts to turn this slow-growing state into a Texas-like economic powerhouse—and serve as a model for Republican leaders in other states.

So far, the results are serving as more of a warning than a beacon. Employment growth is below the national average, while Kansas faces plunging revenue, dwindling reserves and a rare debt downgrade.